Skip to main content Accessibility help
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

2 results

  • Rare event probabilities in random geometric graphs

  • Part of
  • Prabhanka Deka, Fangzhou Luo, Baichuan Wu
  • Journal:
    Advances in Applied Probability , First View
    Published online by Cambridge University Press:
    14 September 2026, pp. 1-27
    • Article
      • You have access
    • PDF
    • HTML
    • Export citation

  • We study rare events in spherical and Gaussian random geometric graphs in high dimensions. In these models, the vertices correspond to points sampled uniformly at random on the d-dimensional unit sphere or correspond to d-dimensional standard Gaussian vectors, and edges are added between two vertices if the inner product between their corresponding points is greater than a threshold $t_{p}$, chosen such that the probability of having an edge is equal to p. We focus on two problems: (a) the probability that the random geometric graph is a complete graph and (b) the probability of observing an atypically large number of edges. We obtain asymptotically exponential decay rates depending on n and d of the probabilities of these rare events through a combination of geometric and probabilistic arguments.

High-Dimensional Probability
  • An Introduction with Applications in Data Science
  • 2nd edition
  • Roman Vershynin
  • Published online:
    30 January 2026
    Print publication:
    19 February 2026
  • 'High-Dimensional Probability,' winner of the 2019 PROSE Award in Mathematics, offers an accessible and friendly introduction to key probabilistic methods for mathematical data scientists. Streamlined and updated, this second edition integrates theory, core tools, and modern applications. Concentration inequalities are central, including classical results like Hoeffding's and Chernoff's inequalities, and modern ones like the matrix Bernstein inequality. The book also develops methods based on stochastic processes – Slepian's, Sudakov's, and Dudley's inequalities, generic chaining, and VC-based bounds. Applications include covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, and machine learning. New to this edition are 200 additional exercises, alongside extra hints to assist with self-study. Material on analysis, probability, and linear algebra has been reworked and expanded to help bridge the gap from a typical undergraduate background to a second course in probability.